Galil Motion Control CDS-3310, User Manual

Page: 131 / 166

70
•
Chapter 10 Theory of Operation CDS-3310
Motor-Amplifier
The current drive generates a current I, which is proportional to the input voltage, V, with a gain of Ka.
The resulting transfer function in this case is
P/V = Ka Kt / Js2
where Kt and J are as defined previously. For example, a current amplifier with Ka = 2 A/V with the
motor described by the previous example will have the transfer function:
P/V = 1000/s2 [rad/V]
If the motor is a DC brushless motor, it is driven by an amplifier that performs the commutation. The
combined transfer function of motor amplifier combination is the same as that of a similar brush
motor, as described by the previous equations.
K
a
K
t
JS
1
S
V
I W P
CURRENT SOURCE
Figure 10.6 - Mathematical model of the motor and amplifier
Encoder
The encoder generates N pulses per revolution. It outputs two signals, Channel A and B, which are in
quadrature. Due to the quadrature relationship between the encoder channels, the position resolution is
increased to 4N quadrature counts/rev.
The model of the encoder can be represented by a gain of
Kf = 4N/2
π
[count/rad]
For example, a 1000 lines/rev encoder is modelled as
Kf = 638
DAC
The DAC or D-to-A converter converts a 16-bit number to an analog voltage. The input range of the
numbers is 65536 and the output voltage range is +/-10V or 20V. Therefore, the effective gain of the
DAC is
K= 20/65536 = 0.0003 [V/count]
Digital Filter
The digital filter has three element in series: PID, low-pass and a notch filter. The transfer function of
the filter. The transfer function of the filter elements are: